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High-order expansion of the solution of preliminary orbit determination problem

High-order expansion of the solution of preliminary orbit determination problem
High-order expansion of the solution of preliminary orbit determination problem
A method for high-order treatment of uncertainties in preliminary orbit determination is presented. The observations consist in three couples of topocentric right ascensions and declinations at three observation epochs. The goal of preliminary orbit determination is to compute a trajectory that fits with the observations in two-body dynamics. The uncertainties of the observations are usually mapped to the phase space only when additional observations are available and a least squares fitting problem is set up. A method based on Taylor differential algebra for the analytical treatment of observation uncertainties is implemented. Taylor differential algebra allows for the efficient computation of the arbitrary order Taylor expansion of a sufficiently continuous multivariate function. This enables the mapping of the uncertainties from the observation space to the phase space as high-order multivariate Taylor polynomials. These maps can then be propagated forward in time to predict the observable set at successive epochs. This method can be suitably used to recover newly discovered objects when a scarce number of measurements is available. Simulated topocentric observations of asteroids on realistic orbits are used to assess the performances of the method
0923-2958
331-352
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Di Lizia, Pierluigi
f86916ba-a73b-42a9-8247-558335c21f22
Lavagna, Michele
3cf16dda-0944-459d-babb-7ba8ae432c65
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Di Lizia, Pierluigi
f86916ba-a73b-42a9-8247-558335c21f22
Lavagna, Michele
3cf16dda-0944-459d-babb-7ba8ae432c65

Armellin, Roberto, Di Lizia, Pierluigi and Lavagna, Michele (2012) High-order expansion of the solution of preliminary orbit determination problem. Journal of Celestial Mechanics and Dynamical Astronomy, 112 (3), 331-352. (doi:10.1007/s10569-012-9400-8).

Record type: Article

Abstract

A method for high-order treatment of uncertainties in preliminary orbit determination is presented. The observations consist in three couples of topocentric right ascensions and declinations at three observation epochs. The goal of preliminary orbit determination is to compute a trajectory that fits with the observations in two-body dynamics. The uncertainties of the observations are usually mapped to the phase space only when additional observations are available and a least squares fitting problem is set up. A method based on Taylor differential algebra for the analytical treatment of observation uncertainties is implemented. Taylor differential algebra allows for the efficient computation of the arbitrary order Taylor expansion of a sufficiently continuous multivariate function. This enables the mapping of the uncertainties from the observation space to the phase space as high-order multivariate Taylor polynomials. These maps can then be propagated forward in time to predict the observable set at successive epochs. This method can be suitably used to recover newly discovered objects when a scarce number of measurements is available. Simulated topocentric observations of asteroids on realistic orbits are used to assess the performances of the method

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More information

Published date: 2012
Organisations: Aeronautics, Astronautics & Comp. Eng

Identifiers

Local EPrints ID: 360788
URI: https://eprints.soton.ac.uk/id/eprint/360788
ISSN: 0923-2958
PURE UUID: 9fc3380d-cb0e-4b3c-b205-2fedb0a698af

Catalogue record

Date deposited: 23 Dec 2013 08:49
Last modified: 16 Jul 2019 21:15

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